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Existence and multiplicity result for a class of second order elliptic equations


Hofer, Helmut (1981). Existence and multiplicity result for a class of second order elliptic equations. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 88(1-2):83-92.

Abstract

SynopsisSome second order semilinear elliptic boundary value problems of the Ambrosetti-Prodi-type are studied. Existence and multiplicity of solutions is proved in dependence on a parameter. Constructing a global strongly increasing fixed point operator in a suitable function space, observing - under appropriate conditions, which are in some sense optimal–that the fixed point operator has some properties similar to a strongly positive linear endomorphism, one unifies and improves the treatment of such problems, whether the nonlinearity is dependent on the gradient or not, and obtains some new results.

Abstract

SynopsisSome second order semilinear elliptic boundary value problems of the Ambrosetti-Prodi-type are studied. Existence and multiplicity of solutions is proved in dependence on a parameter. Constructing a global strongly increasing fixed point operator in a suitable function space, observing - under appropriate conditions, which are in some sense optimal–that the fixed point operator has some properties similar to a strongly positive linear endomorphism, one unifies and improves the treatment of such problems, whether the nonlinearity is dependent on the gradient or not, and obtains some new results.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:1 January 1981
Deposited On:01 Nov 2018 14:12
Last Modified:15 Apr 2021 14:50
Publisher:Cambridge University Press
ISSN:0308-2105
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s0308210500017303

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